Solve the following trigonometric equation for 0to2pi
(a) cos(4x) - 9 sin(2x) + 4 = 0

x = pi/12, 5pi/12, 13pi/12, 17pi/12.

Step-by-step explanation:

Note that cos (4x) =  1 - 2sin^2 (2x)

Substituting we have:

1 - 2sin^2 (2x) - 9 sin(2x) + 4 = 0

2 sin^2 (2x) + 9 sin(2x) - 5 = 0

(2 sin 2x - 1 )(sin 2x + 5 ) = 0

sin 2x = 1/2 and sin 2x = -5.

sin 2x = 1/2,   gives 2x = pi/6, 5pi/6, 13pi/6, 17pi/6.

There are no solutions to sin 2x = -5  because the range of sin x  is -1 to +1.

So x = pi/12, 5pi/12, 13pi/12, 17pi/12.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.